More than 170 victims of alleged physical and sexual abuse who attended a Yorkshire children's home are awaiting the outcome of a dispute between Catholic organisations about who is responsible for paying compensation, the supreme court has heard.

The Roman Catholic diocese of Middlesbrough is seeking to overturn a ruling that it alone must meet claims brought by those who say they were assaulted at St William's children's care home and school in Market Weighton, east Yorkshire.

The allegations date back as far as 1958. The former headmaster James Carragher has twice been convicted of a series of indecent assaults, buggery and taking photographs of young boys.

In 2004 he was sentenced to 14 years in prison, having already served a seven-year sentence imposed in 1993. He has since been expelled by the De La Salle order of Christian Brothers, whose members taught at the institution.

The diocese maintains it should be held only partly responsible for the compensation. The main burden of "vicarious liability" for wrongdoing, it says, should fall on the De La Salle Brothers, since they were in day-to-day charge of operating St William's.

Lawyers for the victims have accused the Catholic church of delaying, or attempting to avoid, compensation payments. In advance of the two-day supreme court hearing, David Greenwood, of Jordans solicitors, said: "The Catholic church has for years tried to escape liability for its priests and members, and I hope this case will decide the issues once and for all.

"One of the Catholic organisations is trying to escape responsibility. I am certain that either the Roman Catholic diocese of Middlesbrough or the De La Salle Institute are responsible for compensating victims."

Lawyers involved in a series of other compensation cases against various Catholic church institutions are watching this test case in the hope that the extent of "vicarious liability" – the responsibility of employers and other organisations for the acts of their workers or volunteers – will be legally defined. In many of the abuse cases, the facts of what occurred have yet to be established.

The diocese of Portsmouth recently lost a related case in the appeal court after denying that it directly employed a priest who was said to have abused a young woman. The final decision is likely to have repercussions far beyond immediate questions over the running of Catholic care homes, and could affect companies' and charities' wider liabilities.

At St William's, more than 20 De La Salle Brothers were the subject of abuse complaints, the supreme court was told, with more than 120 allegations made against Brother Carragher alone.

George Leggatt QC, for the diocese of Middlesbrough, told the court two different groups could be vicariously liable for acts of abuse. He argued that it was wrong to equate employment with responsibility. Some of the legal argument revolved around the origins of the law in master/servant relationships.

A statement issued by the Middlesbrough diocese at the start of the case said the diocese wanted the question of liability cleared up. "Any abuse which occurred is utterly deplorable," it said. "The diocese and its insurers have never sought to avoid or delay the payment of compensation to victims with valid claims but to seek clarity about who should make those payments.

"We have always argued that, as the nominal employers, we are partially liable. But it is right that the main liability should lie with the organisation which ran the school.The De La Salle Brothers appointed the staff and made all the decisions in respect of the running of St William's, and it is right that they should share the cost of compensating victims."